letters to nature NATURE | VOL 412 | 2 AUGUST 2001 | www.nature.com 517 Evaluation of the total entropy For a given r, S at T �� T0 �� 4 000 K is calculated using thermodynamic integration. We first find the free energy difference between an ideal gas and a binary mixture Lennard- Jones (LJ) system at the chosen r by integrating the excess pressure along an isotherm from the high-V limit where the system behaves as an ideal gas. We then carry out a set of simulations at constant V and T that continuously convert the LJ system to BKS silica, by using a hybrid potential f �� lfBKS �� ��1 2 l��fLJ (ref. 33). An appropriate thermody- namic integration from l �� 0 to 1 yields the free energy of BKS silica, from which S at T0 and the chosen r is calculated. The value of S at other temperatures is found by further thermodynamic integration at constant V. Evaluation of the vibrational entropy We evaluate Sharm from the spectrum of eigenfrequencies n (that is, the vibrational density of states) calculated from the inherent structures at each T, using Sharm �� kS 3N i��1��1 2 log��hni =kT����, where k and h are Boltzmann���s and Planck���s constants, respec- tively. To obtain Sanh we use Eanh. We evaluate Eanh �� E 2 Eharm 2 eIS and then fit Eanh with a polynomial constrained to be zero and have zero slope at T �� 0. Assuming that the shapes of the basins do not depend on eIS, Sanh may be calculated by thermodynamic integration using the fitted form of Eanh from T �� 0 to the desired T. In terms of the above quantities, the integration constant in equation (2) is thus Sc0 �� S��T0�� 2 Sanh ��T0�� 2 Sharm ��T0 ��. Isochoric invariance of basin shape Our assumption that the shape of the basins is independent of eIS along an isochore is based on two observations. First we find that the vibrational density of states (the n spectrum), is independent of eIS along an isochore. Second, the anharmonic energy of inherent structure configurations heated from T �� 0 to a chosen T follows the Eanh �� E 2 Eharm 2 eIS curve calculated from equilibrium simulations. This is only possible if the anharmonic character of the basins is also to a large extent independent of eIS. Received 12 April accepted 18 June 2001. 1. Angell, C. A. Relaxation in liquids, polymers and plastic crystals���Strong/fragile patterns and problems. J. Non-Cryst. Solids 131���133, 13���31 (1991). 2. Richet, P. Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48, 471��� 483 (1984). 3. Sciortino, F., Kob, W. & Tartaglia, P. Inherent structure entropy of supercooled liquids. Phys. Rev. Lett. 83, 3214���3217 (1999). 4. Buechner, S. & Heuer, A. The potential energy landscape of a model glass former: thermodynamics, anharmonicities, and finite size effects. Phys. Rev. E 60, 6507���6518 (1999). 5. Sastry, S. The relationship between fragility, configurational entropy and the potential energy landscape of glass-forming liquids. Nature 409, 164���167 (2001). 6. Martinez, L.-M. & Angell, C. A. A thermodynamic connection to the fragility of glass-forming liquids. Nature 410, 663���667 (2001). 7. Adam, G. & Gibbs, J. H. On the temperature dependence of cooperative relaxation properties in glass- forming liquids. J. Chem. Phys. 43, 139���146 (1965). 8. Stillinger, F. H. & Weber, T. A. Packing structures and transitions in liquids and solids. Science 225, 983���989 (1984). 9. Stillinger, F. H. A topographic view of supercooled liquids and glass formation. Science 267, 1935��� 1939 (1995). 10. Sciortino, F. & Tartaglia, P. Extension of the fluctuation-dissipation theorem to the physical aging of a model glass-forming liquid. Phys. Rev. Lett. 86, 107���111 (2001). 11. Starr, F. W., Sastry, S., La Nave, E., Scala, S., Stanley, H. E. & Sciortino, F. Thermodynamic and structural aspects of the potential energy surface of simulated water. Phys. Rev. E 63, 041201 (2001). 12. Rossler, E., Hess, K.-U. & Novikov, V. N. Universal representation of viscosity in glass forming liquids. J. Non-Cryst. Solids 223, 207���222 (1998). 13. Hess, K.-U., Dingwell, D. B. & Rossler, E. Parametrization of viscosity���temperature relations of aluminosilicate melts. Chem. Geol. 128, 155���163 (1996). 14. Barrat, J.-L., Badro, J. & Gillet, P. A strong to fragile transition in a model of liquid silica. Molecular Simulation 20, 17���25 (1997). 15. Horbach, J. & Kob, W. Static and dynamic properties of a viscous silica melt. Phys. Rev. B 60, 3169��� 3181 (1999). 16. Van Beest, B. W. H., Kramer, G. J. & van Santen, R. A. Force fields for silicas and aluminophosphates based on ab initio calculations. Phys. Rev. Lett. 64, 1955���1958 (1990). 17. Speedy, R. J. Relations between a liquid and its glasses. J. Phys. Chem. B 103, 4060���4065 (1999). 18. Hemmati, M., Moynihan, C. T. & Angell, C. A. Density maxima and minima, and water-like heat capacity and transport anomalies, in liquid BeF2. J. Chem. Phys. (in the press). 19. Angell, C. A. Water II is a strong liquid. J. Phys. Chem. 97, 6339���6341 (1993). 20. Speedy, R. J. The hard sphere glass transition. Mol. Phys. 95, 169���178 (1998). 21. Scala, A., Starr, F. W., La Nave, E., Sciortino, F. & Stanley, H. E. Configurational entropy and diffusivity of supercooled water. Nature 406, 166���169 (2000). 22. Johari, G. P. Contributions to the entropy of a glass and liquid, and the dielectric relaxation time. J. Chem. Phys. 112, 7518���7523 (2000). 23. Goldstein, M. Viscous liquids and the glass transition: sources of the excess heat capacity. J. Chem. Phys. 51, 3728���3739 (1969). 24. Coluzzi, B., Parisi, G. & Verrocchio, P. Thermodynamical liquid-glass transition in a Lennard-Jones binary mixture. Phys. Rev. Lett. 84, 306���309 (2000). 25. Bell, R. J. & Dean, P. The configurational entropy of vitreous silica in the random network theory. Phys. Chem. Glasses 9, 125���127 (1968). 26. Speedy, R. J. & Debenedetti, P. G. The distribution of tetravalent network glasses. Mol. Phys. 88, 1293��� 1316 (1996). 27. Stillinger, F. H., Debenedetti, P. G. & Sastry, S. Resolving vibrational and inherent structural contributions to isothermal compressibility. J. Chem. Phys. 109, 3983���3988 (1998). 28. Jagla, E. A. Fragile-strong transitions and polyamorphism in glass forming fluids. Mol. Phys. 99, 753��� 757 (2001). 29. Saika-Voivod, I., Sciortino, F. & Poole, P. H. Computer simulation of liquid silica: equation of state and liquid���liquid phase transition. Phys. Rev. E 63, 011202 (2001). 30. Sastry, S., Debenedetti, P. G., Sciortino, F. & Stanley, H. E. Singularity-free interpretation of the thermodynamics of supercooled water. Phys. Rev. E 63, 6144���6154 (1996). 31. Rebelo, L. P. N., Debenedetti, P. G. & Sastry, S. Singularity-free interpretation of the thermodynamics of supercooled water. II. Thermal and volumetric behavior. J. Chem. Phys. 109, 626���633 (1998). 32. Poole, P. H., Grande, T., Angell, C. A. & McMillan, P. F. Polymorphic phase transitions in liquids and glasses. Science 275, 322���323 (1997). 33. Mezei, M. & Beveridge, D. L. Free energy simulations. Ann. NY Acad. Sci. 482, 1���23 (1986). 34. Scheidler, P., Kob, W., Latz, A., Horbach, J. & Binder, K. Frequency-dependent specific heat of silica. Phys. Rev. B 63, 104204 (2001). 35. Sastry, S., Debenedetti, P. G. & Stillinger, F. H. Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid. Nature 393, 554���557 (1998). 36. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259���267 (2001). Acknowledgements We thank C. A. Angell, W. Kob, S. Sastry and R. Speedy for discussions. I.S.-V. and P.H.P. thank NSERC (Canada) for financial support, and SHARCNET for computing resources. F.S. acknowledges support from the INFM ���Iniziativa Calcolo Parallelo��� and PRE-HOP and from MURST PRIN 2000. Correspondence and requests for materials should be addressed to P.H.P. (e-mail: poole@cmrg.apmaths.uwo.ca). ................................................................. Growth dynamics of pentacene thin films Frank-J. Meyer zu Heringdorf, M. C. Reuter & R. M. Tromp IBM T.J. Watson Research Center, Yorktown Heights, PO Box 218, New York 10598, USA .............................................................................................................................................. The recent demonstration of single-crystal organic optoelectro- nic devices has received widespread attention1���4. But practical applications of such devices require the use of inexpensive organic films deposited on a wide variety of substrates. Unfortu- nately, the physical properties of these organic thin films do not compare favourably to those of single-crystal materials. More- over, the basic physical principles governing organic thin-film growth and crystallization are not well understood. Here we report an in situ study of the evolution of pentacene thin films, utilizing the real-time imaging capabilities of photoelectron emission microscopy. By a combination of careful substrate preparation and surface energy control, we succeed in growing thin films with single-crystal grain sizes approaching 0.1 milli- metre (a factor of 20���100 larger than previously achieved), which are large enough to fully contain a complete device. We find that organic thin-film growth closely mimics epitaxial growth of inorganic materials, and we expect that strategies and concepts developed for these inorganic systems will provide guidance for the further development and optimization of molecular thin-film devices. ���Plastic transistors��� offer possibilities for flexible displays, and all- plastic smart cards and badges, as well as light-emitting diodes and lasers1,5���8. Pentacene (C14H22), a chain-like aromatic molecule composed of five benzene rings, is among the most promising materials. Recent progress in organic electronics has focused on the exploration of new devices in single-crystal materials1���4,9. However, electrical properties of polycrystalline films are inferior to those of single-crystal materials, and���because the mobility in single-crystal bulk material is higher5 than the values reported for organic thin- film transistors (OTFTs)���improvement of the film quality is mandatory10. �� 2001 Macmillan Magazines Ltd

letters to nature 518 NATURE | VOL 412 | 2 AUGUST 2001 | www.nature.com The different types of electrically active traps in pentacene devices have been analysed recently11. Defects inside grains of polycrystal- line films result in Fermi-level pinning, and primarily affect the transistor threshold voltage. Grain boundaries, in contrast, generate charge barriers that have to be overcome by thermionic emission. This does not only explain gate-voltage-dependent mobilities in OTFTs12,13, but also implies that improved device performance may be expected if the grain-boundary density can be reduced by improvements in the thin-film growth process. Previous studies of the growth of pentacene thin films include X- ray investigations of the molecular order6, atomic force microscopy7 and low-coverage scanning tunnelling microscopy14, as well as theoretical studies of the adsorption of single pentacene molecules on surfaces15. The results show that the molecule initially lies flat on the surface14. When several molecules have formed a stable island, they tilt out of the surface plane, and at room temperature form a unique thin-film phase6. The triclinic pentacene bulk structure16 is formed only during growth at elevated temperature2. Here we use low-energy electron microscopy (LEEM)17���19 to investigate the growth of pentacene thin films during in situ deposition. The IBM LEEM II instrument20 was mostly operated in the ���photoelectron emission microscopy��� mode (PEEM), using photoelectrons generated by ultraviolet radiation from a mercury discharge lamp. This allows a field of view of up to 65 mm with a resolution of 125 nm, limited by the pixel resolution of the video camera. The ultraviolet radiation causes the pentacene to desorb on a timescale of minutes. A computer-controlled shutter limits the ultraviolet exposure to 1 second when a PEEM image is taken once every minute, ensuring that film damage is negligible in our experiments. Pentacene was deposited from a quartz crucible heated to ,250 8C. Clean material was obtained by carefully outgassing the pentacene in ultrahigh vacuum before deposition. Without this procedure, charge traps were introduced into the pentacene film as observed with LEEM. In a number of experiments, the sample was exposed to cyclohexene before the growth of pentacene films on it. Cyclohexene (C6H10), a liquid at room temperature, was purified by a repeated number of freeze���pump���thaw cycles. All depositions were done at room temperature. In the PEEM images, contrast between pentacene in the first few molecular layers arises from differences in electronic structure. The first molecular layer appears bright on a dark Si surface (Fig. 1a). In Fig. 1b, the second molecular layer appears dark on the first layer, and in Fig. 1c the third layer appears darker still. With increasing film thickness, contrast disappears as the electronic properties of the surface layer approach those of the bulk. During the initial stages of growth, stable two-dimensional islands nucleate on the surface. The nucleation density depends on the deposition rate and on the preparation of the substrate. Whereas the nucleation density on clean silicon surfaces is of the order of 10-3 mm-2, it can easily be 100 times larger on SiO2. Figure 2 shows the evolution of three pentacene islands on Si(001) during growth at a rate of 10-2 monolayers per minute (one monolayer (ML) is defined as a single molecular layer of crystalline pentacene with a thickness of ,15 A). �� Low-energy electron microdiffraction shows that each island forms a pentacene single crystal, and that the three crystals in Fig. 2a are rotated by a random angle with respect to each other. With increasing coverage the islands grow (Fig. 2b) and a second layer nucleates (arrows in Fig. 2c), while the first-layer islands still avoid touching. In Fig. 2d, trenches between islands are almost filled in, leaving grain boundaries that will eventually affect the electrical transport properties. The fractional layer coverage during growth on clean Si(001) is plotted in Fig. 3a. After deposition is started, it takes several minutes before nucleation occurs. During this dead-time, about one-fifth of a monolayer of pentacene is deposited. Comparison with results from scanning tunnelling microscopy10 indicates that pentacene molecules are adsorbed flat on the surface during the dead-time, and that the islands shown in Fig. 2a nucleate on top of this layer. We believe that this initial layer reacts with, and becomes immobilized by, the high density of reactive dangling bonds on the clean Si(001)(2 �� 1) surface. After nucleation, the first layer grows linearly with time until, at a coverage of 60%, islands nucleate in the second layer. Again, when the coverage in this layer reaches 60%, nucleation in the third layer takes place, showing steady-state layer-by-layer growth. Removal of the clean-surface dangling bonds should remove the initial dead-time, and force immediate nucleation of the first layer. Recent experiments show that adsorption of cyclopentene on Si(001) passivates all dangling bonds21, and that adsorption of cyclohexene on germanium gives similar results22. The layer cover- age for growth of pentacene on cyclohexene-saturated Si(001) is plotted in Fig. 3b. As expected, no dead-time is observed. Other substrates without dangling bonds, such as thermal SiO2 grown in situ, also show no dead-time. In all three cases discussed above, the well defined and highly uniform initial surfaces result in much lower nucleation densities (that is, larger grain sizes) than pre- viously observed. This improvement in grain size is in large measure due to the absence of heterogeneous nucleation in our experiments. In contrast, we find that growth on poorly controlled oxide surfaces is dominated by dense heterogeneous nucleation. Growth of the initial molecular layers is controlled by a number of factors. The presence of reactive sites on the surface may give rise to an initial dead-time. Beyond that, the homogeneous nucleation density of the first crystalline molecular layer, N1, is determined by the ratio F/Ds, where F is the growth rate and Ds is the diffusion constant of pentacene on the substrate. Nucleation of the second layer takes place when the first layer islands exceed a critical size Rc���which depends on F, the diffusion constant of pentacene on pentacene Dp, and the excess diffusion barrier at the island step-edge, EB (the so-called Ehrlich-Schwoebel barrier)23. When pRcN1 2 , 1, second-layer nucleation occurs before the first layer closes24. As Ds and Dp are not identical, N1 depends on the substrate, whereas Rc does not. As the initial nucleation density increases, the coverage at which a new layer nucleates changes from 0.6 for clean Si(001) to 0.8 for SiO2. However, the resulting improvement in 15 ��m a b c Figure 1 a���c, Development of the pentacene layer-by-layer contrast during deposition. a, One layer b, two layers c, three layers. Scale bar applies to all panels. �� 2001 Macmillan Magazines Ltd